February 10, 2022 by Teamrat A. Ghezzehei

### Water Retention Lessons in Desmos

#### Visual Fitting van Genuchten Water Retention Model

The *van Genuchten* (1980) model is the most widely used water retention curve function:

where the $\theta_s$ and $\theta_r$ are satuarted and residual water content, respectively; and $\alpha$ and $n$ are shape parameters; and $m=1-/n$. In the Desmos the four can be changed independentky using sliders.

This demonstration includes three example soils from the UNSODA database to illustrate how the van Genuchten parameteric model can be fitted to the data. The goodness of fit of the model is described using sum of squared errors (SSE):

\[E = \sum{(\theta_{model} - \theta_{data})^2}\]The SSE of the three example soils are diplayed below the paramaters. As you adjust the parameters watch how the SSE of your traget soil reflects the proximity of the model to the data.

**Example Soils** UNSODA CODE (Texture)

- 1042 (Sandy)
- 1352 (Silt Loam)
- 1381 (Loam)

#### Predicting van Genuchten parameters uisng pedotransfer function

The Rawls and Brakensiek (1985) *Pedotransfer Function* is one of the oldest and widely used regression models used to predict the parameters of the van Genuchten model from texture and porosity data. It uses a multi-regression equation. The required inputs are Sand content ($S$), Clay content ($C$), and porosity.

#### References

- Rawls, Walter J., and Donald L. Brakensiek. “Prediction of soil water properties for hydrologic modeling.” Watershed management in the eighties. ASCE, 1985

#### Exercise

Test the accuracy and limitations of of the pedotransfer function by predicting the parameters of the three soils included in the first desmos module. The sand, clay, and porosity values you need to predict the parameters are given below.

**Example Soils** UNSODA CODE (Sand%, Clay%, Porosity)

- 1042 (96,3, 0.39)
- 1352 (14.3, 17.4, 0.38)
- 1381 (45.8, 11.2, 0.354)